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Probl. Anal. Issues Anal., 2014, Volume 3(21), Issue 2, Pages 3–15 (Mi pa179)  

About planar $(\alpha,\beta)$–accessible domains

K. F. Amozova, E. G. Ganenkova

Petrozavodsk State University, Lenin Avenue, 33, 185910 Petrozavodsk, Russia

Abstract: The article is devoted to the class $A^{\alpha,\beta}_{\rho}$ of all $(\alpha,\beta)$–accessible with respect to the origin domains $D,$ $\alpha,\beta\in[0,1),$ possessing the property\thinspace $\rho=\min\limits_{p\in\partial D}|p|,$\thinspace where\thinspace $\rho\thinspace\in \thinspace(0,+\infty)$ is a fixed number. We find the maximal set of points $a$ such that all domains $D\in A^{\alpha,\beta}_{\rho}$ are $(\gamma,\delta)$–accessible with respect to $a,$ $\gamma\in[0;\alpha],$ $\delta\in[0;\beta]$. This set is proved to be the closed disc of center $0$ and radius $\rho\sin\displaystyle\frac{\varphi\pi}{2},$ where $\varphi=\min\{\alpha-\gamma,\beta-\delta\}$.

Keywords: $\alpha$–accessible domain, $(\alpha,\beta)$–accessible domain, cone condition

DOI: https://doi.org/10.15393/j3.art.20014.2689

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Document Type: Article
MSC: 52A30, 03E15
Received: 03.09.2014
Language: English

Citation: K. F. Amozova, E. G. Ganenkova, “About planar $(\alpha,\beta)$–accessible domains”, Probl. Anal. Issues Anal., 3(21):2 (2014), 3–15

Citation in format AMSBIB
\Bibitem{AmoGan14}
\by K.~F.~Amozova, E.~G.~Ganenkova
\paper About planar $(\alpha,\beta)$--accessible domains
\jour Probl. Anal. Issues Anal.
\yr 2014
\vol 3(21)
\issue 2
\pages 3--15
\mathnet{http://mi.mathnet.ru/pa179}
\crossref{https://doi.org/10.15393/j3.art.20014.2689}
\elib{http://elibrary.ru/item.asp?id=22927219}


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